Magnetic Quantum Oscillations of the Longitudinal Conductivity $\sigma_{zz}$ in Quasi two-dimensional Metals

TL;DR

This paper derives an analytical expression for the longitudinal magnetoconductivity in layered conductors under high magnetic fields, revealing unusual temperature and field dependencies and a pseudo-gap phenomenon relevant to organic conductors.

Contribution

It provides a novel analytical framework for understanding magnetoconductivity in quasi-2D metals with impurity scattering under strong magnetic fields.

Findings

Unusual temperature and magnetic field dependence of Shubnikov-de Haas oscillations.

Appearance of a pseudo-gap in zero-temperature magnetoconductivity.

Thermally activated behavior of conductivity minima at low temperatures.

Abstract

We derive an analytical expression for the longitudinal magnetoconductivity $\sigma_{zz}$ in layered conductors in presence of a quantizing magnetic field perpendicular to the layers and for short-range in-plane impurity scattering in frame of the quantum transport theory. Our derivation points out quite unusual temperature and magnetic field dependences for Shubnikov-de Haas oscillations in the two-dimensional limit, i.e. $\hbar \omega_{c} \gg 4 \pi t$, where $t$ is the interlayer hopping integral for electrons, and $\omega_{c}$ the cyclotron frequency. In particular, when $\hbar \omega_{c} \gg 4 \pi t$ and $\hbar \omega_{c} \geq 2 \pi \Gamma_{\mu}$ (here $\Gamma_{\mu}$ is the value of the imaginary part of the impurity self-energy at the chemical potential $\mu$), a pseudo-gap centered on integer values of $\mu/\hbar\omega_{c}$ appears in the zero-temperature magnetoconductivity function $\sigma_{zz}(\mu/\hbar\omega_{c})$. At low temperatures, this high-field regime is characterized by a thermally activated behavior of the conductivity minima (when chemical potential $\mu$ lies between Landau levels) in correspondence with the recent observation in the organic conductor $\beta''\text{-(BEDT-TTF)}_{2}\text{SF}_{5}\text{CH}_{2}\text{CF}_{2}\text{SO}_ {3}$.